Open Access Research article

A simple ratio-based approach for power and sample size determination for 2-group comparison using Rasch models

Véronique Sébille1*, Myriam Blanchin1, Francis Guillemin2, Bruno Falissard34 and Jean-Benoit Hardouin1

Author Affiliations

1 EA 4275, Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences, University of Nantes, Nantes, France

2 EA 4360 Apemac, Lorraine University, Paris Descartes University, Nancy, France

3 INSERM 669, Université Paris-Sud and Université Paris Descartes, Paris, France

4 AP-HP, Hôpital Paul Brousse, Département de santé publique, Villejuif, France

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BMC Medical Research Methodology 2014, 14:87  doi:10.1186/1471-2288-14-87

Published: 5 July 2014



Despite the widespread use of patient-reported Outcomes (PRO) in clinical studies, their design remains a challenge. Justification of study size is hardly provided, especially when a Rasch model is planned for analysing the data in a 2-group comparison study. The classical sample size formula (CLASSIC) for comparing normally distributed endpoints between two groups has shown to be inadequate in this setting (underestimated study sizes). A correction factor (RATIO) has been proposed to reach an adequate sample size from the CLASSIC when a Rasch model is intended to be used for analysis. The objective was to explore the impact of the parameters used for study design on the RATIO and to identify the most relevant to provide a simple method for sample size determination for Rasch modelling.


A large combination of parameters used for study design was simulated using a Monte Carlo method: variance of the latent trait, group effect, sample size per group, number of items and items difficulty parameters. A linear regression model explaining the RATIO and including all the former parameters as covariates was fitted.


The most relevant parameters explaining the ratio’s variations were the number of items and the variance of the latent trait (R2 = 99.4%).


Using the classical sample size formula adjusted with the proposed RATIO can provide a straightforward and reliable formula for sample size computation for 2-group comparison of PRO data using Rasch models.

Patient-reported outcomes; Item response theory; Rasch model; Sample size; Power